List of top Questions asked in GATE MN

The metal that belongs to Rare Earth Element category is
The safety device used to arrest forward runaway tubs in rope haulage is
The rank of \(3 \times 3\) matrix \(A\) is 2. The determinant of the matrix is
If \( y = x^x \), then \( \frac{dy}{dx} \) is:
A steeply dipping metalliferous ore body is non-susceptible to spontaneous heating. The blasted ore is used as the platform to work in a stope. Appropriate mining method for this orebody is
A non-transit theodolite does NOT have
A wastewater sample has an ultimate BOD of 300 mg/L. BOD reaction rate constant is 0.22 per day at 20 ℃. If the temperature coefficient is 1.05, the 5-day BOD at 25 ℃, in mg/L, is:
The directional derivative of a function \( f(x, y, z) = 4x^2 + 8y^2 + 9z^2 \) at the point \( P(3, 4, 5) \) in the direction vector \( \vec{b} = 2\hat{i} - 3\hat{j} + 4\hat{k} \) is _______ (rounded off to 1 decimal place).
A mine void of dimension 100.0 m x 2.0 m x 1.2 m is to be filled in 3 hours by hydraulic stowing. The sand to slurry ratio is 0.4. If the hydraulic fill factor is 0.9, the hourly consumption of water for the operation, in m\(^3\), is ________ (rounded off to 2 decimal places).
A pit slope has the following information: Number of benches = 5, Height of each bench = 8 m, Bench slope angle = 70° If the width of one bench is 24 m and that of other four benches is 10 m each, the overall pit slope angle, in degree, is ________ (rounded off to 2 decimal places).
In a surface mine, blasting is carried out using electronic detonator and cartridge emulsion explosive with the following details: Burden = 3.5 m, Spacing = 4.5 m, Bench height = 10.0 m, Subgrade drilling = 1.0 m, Stemming = 4.0 m, Linear charge concentration = 16 kg/m, Cost of one detonator = Rs. 800, Cost of explosive = Rs. 30/kg. The cost of blasting material per cubic meter of blasted rock, in Rs., is ________ (rounded off to 2 decimal places).
The CORRECT statement(s) of dragline operation is/are:
The value of \( \lim_{x \to 0} \left( \frac{\tan 11x}{\tan 5x} \right) \) is:
Hydraulic fracturing method is used to determine the major principal stress (\( \sigma_1 \)) in an underground rock strata having tensile strength of 6 MPa. The minor principal stress (\( \sigma_3 \)) in the strata is 8 MPa. If fluid pressure of 10 MPa is required to fracture the vertical borehole in that strata, the magnitude of \( \sigma_1 \), in MPa, is:
In a depillaring face of an underground coal mine, both wet and dry bulb temperatures are 30 ℃. The relative humidity of the face environment, in percentage, is
In a M/M/1 system, the inter-arrival time of dumpers to a shovel follows exponential distribution with a mean arrival rate of 9 dumpers per hour. The service time of the shovel follows exponential distribution with a mean service rate of 12 dumpers per hour. The probability that exactly one dumper is available to the shovel is
A thermal power plant has an agreement with three mines M1, M2 and M3 to receive 'Grade 1' coal, in the proportion of 60%, 25% and 15%, respectively. The probabilities that a wagon supplied coal to the plant containing below Grade 1' from mines M1, M2 and M3 are 0.02, 0.03 and 0.04, respectively. On a random check, a sample wagon is found to carry below 'Grade 1' coal. The probability that the wagon belongs to mine M1, is____.(round off up to 2 decimals)
In an underground coal mine, two fatalities and three serious bodily injuries occurred during the year 2022. The average daily employment is 1100 and annual working days is 300. The severity index as per DGMS guideline for the mine is
A project network with the sequence of five activities is shown.
A project network with the sequence of five activities
The crashing costs of activities are
ActivityABCDE
Duration (week) 56834
Crashing cost per week (lakh INR)4.02.52.03.04.0
If the project is crashed by one week, the increase in project cost, in lakh INR, is
Four identical districts of a mine are ventilated with a quantity of 3500 m3/min at a fan drift pressure of 1.15 kPa. When one of the districts is sealed off, the change in resultant resistance is 0.072 Ns2m-8. If the fan is stopped, keeping a district sealed, the quantity through the mine becomes 850 m3/min. The natural ventilation pressure in Pa, is
A Bord and Pillar panel is developed at a depth of 250 m in a flat coal seam. The vertical stress gradient is 0.027 MPa/m. If the strength of a square pillar is 12.5 MPa, the extraction ratio of the pillar for a safety factor of 1.5, is____.(round off up to 2 decimals)
Water is pumped from a mine sump at the rate of 300 m3/hr to an inverted conical water tank, as shown. The rate of rise in water level in m/min, at the instant water level reaches at 5 m height from bottom of the tank, is____.(round off up to 2 decimals)
Water is pumped from a mine sump at the rate of 300
A mine worker weighing (W) 600 N lifts an object of 100 N as shown. The 50% body weight is applied downward through point A and a force FE is produced parallel to x axis by the contraction of erector spinae muscle during lifting. The lumber disc, L (shown by red box) acts as a smooth hinge and keeps the upper body in static equilibrium. Ignore all other forces in the body. The magnitude of the resultant of the reaction forces, in N at the lumber disc, is____.(round off up to 2 decimals)
A mine worker weighing (W) 600 N lifts
In an opencast coal mine, blast vibrations are measured at two locations, A and B simultaneously for a maximum charge per delay (Q) of 1200 kg as given.
LocationDistance from the blast face, D (m) PPV (mm/s)
A100 112.5
B30020.3 
\(PPV=K[\frac{D}{\sqrt{Q}}]^{-B}\)
where, K and ẞ are site constants. The PPV in mm/s, at a distance of 200 m from the blast face, is (round off up to 2 decimals) 
A solid ball of mass 10 kg is subjected to forces as shown. The magnitude of the acceleration in m/s2, is____.(round off up to 2 decimals)
A solid ball of mass 10 kg